Zero-size objects in Riemann-Cartan spacetime

TL;DR

This paper investigates the motion of zero-size massive objects in Riemann-Cartan spacetime, revealing a unique spin-curvature interaction and showing that Dirac particle spin decouples from curvature due to its zero size.

Contribution

It introduces a new world line equation for zero-size objects in Riemann-Cartan geometry, highlighting a novel spin-curvature coupling and the decoupling of Dirac spin from curvature.

Findings

Zero-size objects follow a modified world line with spin-curvature coupling.

Dirac particle spin does not couple to background curvature in the zero-size limit.

Wave packet analysis confirms the disappearance of spin and orbital angular momentum in the zero-size limit.

Abstract

We use the conservation law of the stress-energy and spin tensors to study the motion of massive zero-size objects in Riemann-Cartan geometry. The resultant world line equations turn out to exhibit a novel spin-curvature coupling. In particular, the spin of the Dirac particle does not couple to the background curvature. This is a consequence of its truly zero size which consistently rules out the orbital degrees of freedom. As a test of consistency, the wave packet solution of the free Dirac equation is considered. It is shown that the wave packet spin and orbital angular momentum disappear simultaneously in the zero-size limit.